Question: Solve for $x$ : $5x^2 + 40x + 75 = 0$
Explanation: Dividing both sides by $5$ gives: $ x^2 + {8}x + {15} = 0 $ The coefficient on the $x$ term is $8$ and the constant term is $15$ , so we need to find two numbers that add up to $8$ and multiply to $15$ The two numbers $5$ and $3$ satisfy both conditions: $ {5} + {3} = {8} $ $ {5} \times {3} = {15} $ $(x + {5}) (x + {3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 5) (x + 3) = 0$ $x + 5 = 0$ or $x + 3 = 0$ Thus, $x = -5$ and $x = -3$ are the solutions.